2016/11/20 by Nathanaël Hozé, David Holcman, Hoze, Nathanael +1
Computer Science · Environmental Science · #Coagulation and Flocculation Studies #FOS: Mathematics #FOS: Physical sciences #G.2.1 #G.3 G.2.1 #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Statistical and Computational Modeling
paper · pdf · doi:10.48550/arxiv.1611.06493
openalex publication_date 2016/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Coagulation-fragmentation processes describe the stochastic association and\ndissociation of particles in clusters. Cluster dynamics with cluster-cluster\ninteractions for a finite number of particles has recently attracted attention\nespecially in stochastic analysis and statistical physics of cellular biology,\nas novel experimental data is now available, but their interpretation remains\nchallenging. We derive here probability distribution functions for clusters\nthat can either aggregate upon binding to form clusters of arbitrary sizes or a\nsingle cluster can dissociate into two sub-clusters. Using combinatorics\nproperties and Markov chain representation, we compute steady-state\ndistributions and moments for the number of particles per cluster in the case\nwhere the coagulation and fragmentation rates follow a detailed balance\ncondition. We obtain explicit and asymptotic formulas for the cluster size and\nthe number of clusters in terms of hypergeometric functions. To further\ncharacterize clustering, we introduce and discuss two mean times: one is time\ntwo particles spend together before they separate and other is the time they\nspend separated before they meet again for the first time. Finally we discuss\napplications of the present stochastic coagulation-fragmentation framework in\ncell biology.\n